Pre-practicum 1 – Lesson Template

Name: ​Morgan Tobin​ Date: ​12/10/18

School: ​The Lincoln School ​ Grade: ​5

Starting and Ending Time: ​9am to 10am

OVERVIEW OF THE LESSON

MA Curriculum Frameworks incorporating the Common Core State Standards: ​Withregard to how this lesson fits into the “big picture” of the students’ long-term learning, whichMA framework does the lesson most clearly address?

(including mixed numbers) by replacing given fractions with like denominators.

CCSS.MATH.CONTENT.5.NF.A.2Solve word problems involving addition and subtraction of fractions referring to the same whole,including cases of unlike denominators, e.g., by using visual fraction models or equations torepresent the problem. Use benchmark fractions and number sense of fractions to estimatementally and assess the reasonableness of answers. ​For example, recognize an incorrect result2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2​.

Revisit/SolidifyCCSS.MATH.CONTENT.3.NF.A.1- understand a fraction 1/b as the quantity formed by 1 partwhen a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formedby a parts of size 1/b.

CCSS.MATH.CONTENT.3.NF.A.3.B- understand two fractions as equivalent if they are the

CCSS.MATH.CONTENT.4.NF.A.2Compare two fractions with different numerators and different denominators, e.g., by creatingcommon denominators or numerators, or by comparing to a benchmark fraction such as 1/2.Recognize that comparisons are valid only when the two fractions refer to the same whole.Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., byusing a visual fraction model.Standards of Mathematical Practice

CCSS.MATH.PRACTICE.MP1​ Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP3​ Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP4​ Model with mathematics.

CCSS.MATH.PRACTICE.MP6​ Attend to precision.

CCSS.MATH.PRACTICE.MP5​ Use appropriate tools strategically.

Instructional Objective: ​By the end of the lesson, (1) ​what​ concept, information, skill, orstrategy will the students) learn and (2) ​how​ will they demonstrate that knowledge?

SWBAT model addition with fractions with unlike denominators using fraction strips to aid incalculating the sum and visualizing the need for common denominators.

Assessment:​ What specific, tangible evidence will show that each student has met thisobjective?

Students will demonstrate this knowledge as they break off into groups and complete additionproblems at each station (teacher and para will observe and probe during the station rotation, aswell as look at the notes students completed at each station to gain an understanding of studentcomprehension).Students will also complete a written exit ticket in which they must demonstrate either throughwords or models why fractions must have like denominators when adding and subtracting.Academic Language Objective: ​By the end of the lesson, (1) ​what​ ​language​, relating to thelesson and lesson content, will the student(s) know or learn, and (2) ​how​ will they demonstratethat knowledge? Refer to Read Aloud Training (Elementary) or Academic Language Training(Secondary) and to ​WIDA​ and ​Three Tiers of Vocabulary​ Beck, Kucan, and McKeown (2002) ascited by Thaashida L. Hutton in ​Three Tiers of Vocabulary and Education​.

Students will solidify an understanding of the terms “numerator,” “denominator,” “equivalent

fraction,” “whole,” and “ common denominator”.

Students will already be familiar with these terms, because they have found equivalent fractionsin the past and have found common denominators to compare fractions.

Student friendly definitions:

● Numerator: the top number in a fractions that tells how many equal parts there are ● Denominator: the bottom number in a fraction that tells the total number of equal parts the whole is divided in to. ● Equivalent fractions: fractions that represent the same part of a whole. ● Whole: the overall unit that each fraction is referring to. ● Common denominator: denominators of two fractions are equivalent

Assessment:​ What specific, tangible evidence will show that each student has met thisobjective?Student understanding of these terms will be assessed based on student’s ability to use thesewords appropriately in full class and small group discussions. Students will also be expected touse the terms in their exit ticket description.

Content: ​What are the specific details of the lesson’s content knowledge?

​During this lesson, students will learn about the importance of finding common denominatorsbefore adding fractions. Students will understand the concept that in order to add fractions, thefractions need to be in reference to the same object or unit size. It is to be assumed (given theprior content standards in the Common Core), that students already have an understanding ofmaking equivalent fractions and the concept that a fraction a/b is equivalent to a fraction(nxa)/(nxb) (CCSS.MATH.CONTENT.4.NF.A.1). Students will also be familiar with findingcommon denominators to compare fractions, so this lesson will offer another application ofcommon denominators. Students will understand that if you are adding fractions with unlikedenominators you are adding different size pieces. In order to add these fractions, a common unitsize is needed. This will be further illustrated by saying that when adding or subtracting objectssuch as 2 dogs and 1 cat, you can only say that there are 3 animals, not anything specific to thedogs or cats, because you cannot add two different kinds of objects.

PROCEDURES FOR THE LESSON

In this section, provide specific directions, explanations, rationales, questions, potentialvignettes/scenarios, strategies/methods, as well as step-by-step details that could allow someoneelse to​ ​effectively teach the lesson and meet the lesson objectives.

Opening ​(10 minutes)​:​ How will you introduce the instructional objective to the students,pre-teach/ preview vocabulary, and prepare them to engage with the lesson content?

Have 4 groups of 5 students posted on the board and have students sit with their groups and workon a warm-up activity individually.

The lesson will open with a warm-up activity which requires students to add and subtractfractions with like denominators, finding common denominators.

Students will be given about 7 minutes to complete the warm up activity. After completing thewarm up, students will be asked to share their answers with the class, as the teacher explains ifthe student’s proposed solution was correct. If not, be sure to correct students and go over theproblem.

When going over the addition and subtraction problems, remind students not to add/subtract thedenominators of fractions. Reminding students that changing the denominator would change thesize of each unit, thus altering the problem. (Note answers are on attached warm up sheet).

When finding common denominators remind students the procedure: multiplying the twodenominators will create a multiple of both denominators, or check to see if one of thedenominators is already a multiple of the other. After determining what the commondenominator is, multiply the numerator by the same factor as the denominator was multiplied by.Place the new numerator over the common denominator. Also mention that there are manypossible answers for common denominators, because the questions did not specifically ask for aleast common denominator. As long as the denominator is a multiple of both originaldenominators, it is common. Be sure that after the lesson, when checking the students’ warmups, you check that students properly identified common denominators to see which studentsmight still need help with this concept.

During​ ​Lesson ​(40 minutes)​:​ How will you direct, guide, and/or facilitate the learning process tosupport the students in working toward meeting the instructional objectives?

Following the warm up, a scenario will be displayed on the board and guided notes sheets.

The scenario is that as part of a “Stay Active” campaign, the whole class is in a competition tosee what pair of students ran the most miles each week. The students were put in pairs, to holdeach other accountable for running and encourage each other. The success of the pairs rides onthe participation of both students. At the end of the week the teacher asks pairs to add up theirmiles and then report them to the class to see which pair ran the farthest. (This page and thevalues is attached to the end of the lesson plan).

After having students read the scenario by themselves, I will read it aloud and emphasize theseparate addition problems that the problem requires students to answer. I will then ask studentsto work on the first pair’s distance (¾ +½) with their group of 5 (already in their groups from thebeginning of the lesson). Groups will be heterogeneous in terms of math ability (specificallyknowledge of fractions) so that all students can learn from his classmates, but not feel entirelybehind in the group.

After letting groups work on their answer for 3 minutes, I will pull the class back together todiscuss the answer. First I will have each group share their answer and strategy. I expect mostgroups to add both the numerator and denominator to get an answer of 4/6 of a mile for the firstpair. I will then ask students if this answer makes sense. I will tell students to compare theiranswer to the distance Partner A ran (they have experience with this, and will be able to see thatby 4/6 is less than ¾. After determining this, I will emphasize that this does not make sense,because Partner A and Partner B are adding their (positive) distances so the total should begreater than both of the addends.Once this discrepancy has been identified, I will ask if students have any ideas as to why thismethod does not work. I will encourage the students to draw fraction strips to model this.

Next, generalize the procedure for adding fractions with unlike denominators.“When adding and subtracting fractions with unlike denominators, first find a commondenominator for the fractions” (students should already be familiar with this process andreminded through the warm up procedure).

Go through each step of solving this problem: finding the common denominator, ensuringfractions are equivalent to the originals, adding the numerators and placing the sum over thecommon denominator. Converting to a mixed number if necessary. Students should be followingalong on their notes sheet and filling in as the teacher goes through each step. (These steps areincluded for the specific problem on the guided notes.)

After working through the Henry and Georgia pair problem, the teacher will designate a startingpoint for each group and explain that each pair of runners is a different station that students willbe travelling to. The students should be verbally reminded of the rules of respectful andproductive small group work and told that each station will last approximately 6 minutes.

Each station should have cut out fraction strips (3 per student at each station), which studentswill use to divide and visualize the different unit sizes (fractions of different sizes which cannotbe added until they are converted to equivalent fractions with a common denominator) withineach whole (mile).

Students should be allotted 6 minutes at each station, and should be expected to reach aconsensus as a group.

At the teacher’s discretion, he/she can be floating around as groups work, helping as needed andoverseeing discussions. Alternatively, the teacher may choose to remain at the same station(choose a challenging partner most likely SP or CV partner pair ) to help each group at thatstation, modelling how the problems should be thought about and how the group should bediscussing with each other. If there is a para in the room, he/she can take on one of the roles ofcirculating the room and helping groups as question arise in other stations. Be sure that whenworking with students the teacher and para are keeping in mind what students understand aboutfinding common denominators and the use of fraction strips to visualize the different sizes offractions that do not share denominators. Also prompt students to ask questions and persevere ifthey are struggling.

After 25 minutes (6 minutes per station, plus rotating time). The teacher should call the classtogether to review each station.

After groups have settled and the teacher has the attention of the entire class, ask a member ofthe class to share the common denominator they used, the equivalent fractions, and the overallsum. This should be done for each pair of runners and the answers should be written on thewhiteboard.

Once a class consensus is reached about the sum of each pair, each group should be asked todetermine which pair ran the most over the course of the week (at teacher’s discretion acalculator can be used to aid in this comparison task, give students about 5 minutes to do this.)

Following this, have each group share their answers. Depending on if the class reaches aconsensus, the teacher will walk through the comparison.The class should determine that Luis and Maggie ran the longest that week.

Closing ​(10 minutes)​: ​How will you bring closure to the lesson and, by doing so, review anddetermine what students have learned?

Once the class scenario has finished, have students complete their exit tickets individually. Priorto completing the exit ticket, remind students of the terms they should be using in question 1(these are the vocabulary terms in the academic language section).

Once students have complete the exit ticket, collect them and utilize them to assess students’grasp of the lesson objectives and their readiness to move on to the subtracting with unlikedenominators.

FINAL DETAILS OF THE LESSON

Classroom Management:​ If teaching a small group or whole class, how will you use classroomroutines, reinforce appropriate behavior, and/or handle behavioral issues? Give one example.NA

Materials: ​What are the materials that you will need to organize, prepare, and/or try-out beforeteaching the lesson?

● Fraction strips for each student at each station, teacher can decide if pre-divided or not to aid in visualizing whole and different fraction amounts. ● Student Guided notes for each student ● Warm up activity for each student ● Exit ticket for each student ● Reminder of group work rules at each station.Follow-up:​ How will you and/or your Supervising Practitioner reinforce the learning at a latertime so that the students continue to work toward the lesson’s overarching​ ​goal (i.e., the MACurriculum Framework incorporating the Common Core State Standards)?

Based on the exit ticket and student understanding of the concepts taught in this lesson, there willbe a transfer of the idea of calculating common denominators in adding fractions to subtractingfractions. Homework problems can be provided which integrate both adding and subtractingfractions with unlike denominators and continue to have students express why it is necessary tofind common denominators in these situations. Gradually, students can shift away from usingmanipulatives and fraction strips when completing these problems, but early on they helpemphasize the need to find common denominators.Name: Date: WARM-UP 1. Compute the sum/difference using fraction strips if necessary: a. 34 − 14Answer: ​ = 24 = 12

11 5 b. 12 + 12

14 7Answer:​ = 12 = 6 = 1 16

2. Find a common denominator for the fractions below:

*Remember the fractions must be equivalent to the originals. a. 35 & 25 4

Because 25 is a multiple of 5, a common denominator is 25: 3x5=15

15 4 New Fractions: 25 & 25 4 9b. 7 & 10 Because 70 is a multiple of both 7 and 10 that is a common denominator. 4x10= 40; 9x7= 63 40 63 New Fractions: 70 & 70Name: Date: GUIDED NOTES: Adding Fractions with Unlike Denominators Full Class Scenario:As part of a “Stay Active” campaign, the whole class is in a competition to see what pair ofstudents ran the most miles in the past week. The students were put in pairs, to hold each otheraccountable for running. The success of the pairs rides on the participation of both students. Atthe end of the week the teacher asks pairs to add up their miles and report them to the classbelow are the following running distances:

Partner Names Partner A Partner B Pair’s Total Mileage

Henry and Georgia ¾ ½ ¾+½

(HG)

Jack and Luke (JL) ⅓ ¼ ⅓+¼

Luis and Maggie 11/12 ⅔ 11/12 + ⅔

(LM)

Sasha and Patrick ⅚ 3/7 ⅚ + 3/7

(SP)

Carter and Valentina ⅝ 7/9 ⅝ + 7/9

(CV)

What is the “whole” in this problem?

The “whole” is 1 mile.

How many miles did each pair run? Which pair ran the most?HG: ¾+ ½ =5/4= 1 ¼ miles

JL: ⅓ + ¼ = 7/12 of a mile

LM: 11/12 + 2/3 = 19/12= 1 7/12 miles

SP: ⅚ + 3/7= 53/42= 1 11/42 miles

CV: ⅝ + 7/9= 101/72= 1 29/72 miles

How many miles did Henry and Georgia run? (group work)Dependent on groupsHow many miles did Henry and Georgia run? (class discussion)

Henry 1/4

Georgia 1/2

Together Henry and Georgia ran​ ​miles.

1 ¼ milesTo solve this, a common denominators between ½ and ¾ must be found. Because 4 is a multipleof 2, a common denominator is 4. After finding the common denominator the equivalent fractionfor ½ must be found by multiplying the numerator by the same factor as the denominator so ½becomes 2/4. We can then add the numerators 2 and 3 and get an answer of 5/4. We can thenconvert this to a mixed number and discover that Henry and Georgia ran 1 and ¼ miles.

Why can’t we add ¾ and ½ in the form they are written?

We cannot add fractions with different denominators, because they are not of the same size.Even though the whole is a mile, each piece of a mile is not the same, so we cannot generalizethe sum until we find common denominators. Adding fractions with unlike denominators wouldbe like adding cats and dogs and giving the sum in terms of dogs.

Group Work: Station 1: Jack and LukeTogether Jack and Luke ran​ ​miles.7/12 of a mileJL: ⅓ + ¼ = 7/12 of a mileCommon denominator of 12Equivalent fractions ⅓ = 4/12 and 1/4 = 3/124+3=7 7Sum is 12 miles

Which group ran the most miles?

1. Why is it important to find common denominators when adding/subtracting fractions?

Use at least 3 words from the word bank, or use fraction strips as a model.

When adding fractions, it is important that the ​denominators​ of each fraction are the same. Thisis because adding fractions with different denominators means adding different size units. Evenif the ​whole​ is the same, the size of the pieces being added must match both addends. Therefore,when adding fractions with unlike denominators, a ​common denominator​ must be found byfinding ​equivalent fractions​. After common denominators are found, the ​numerators​ can beadded, as would be done in other addition problems with like denominators.

2. Solve the following problem: Amir has ⅝ of a pizza and Jen has ¾ of an identical size pizza. If Amir and Jen combine their pizzas, how many pizzas will the pair have? 5 8 + 34 = ⅝ + 68 = (5+6) 8 = 11 8 = 1 ⅜ of pizza Amir and Jen will have one pizza and 3 extra slices.

3. Thinking Ahead: do you predict you will need to find common denominators when subtracting fractions with unlike denominators? Yes, because just like with adding, you must be subtracting the same type object. If fractions have different denominators they are different sizes and cannot be subtracted or added before finding common denominators.